The motion of membranes in space-time

The equation of a hypersurface interacting with external fields in space-time is established. A class of models is based on the properties of a symmetric divergence-free distribution-valued stress tensor for the interacting system. The elastodynamic properties are encoded into the induced metric and shape tensor of the immersion together with invariants constructed from the Weingarten map. Two particular examples are discussed that are relevant to recent developments in the theories of relativistic extended particles